Is the function y = x + 2 one-to-one?

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Discussion Overview

The discussion centers on whether the function y = x + 2 is one-to-one. Participants explore the characteristics of the function, including its linearity and the implications of its graphical representation.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Mathematical reasoning

Main Points Raised

  • Some participants assert that y = x + 2 is one-to-one because each y-value corresponds to a unique x-value in the domain.
  • Others caution that using specific examples alone does not confirm a function's one-to-one nature, referencing the function y = sqrt(9 - x^2) as a counterexample that fails the horizontal line test.
  • There is a suggestion that visualizing the graph of a function is crucial for determining if it is one-to-one.
  • Participants discuss the importance of the vertical line test in identifying functions.

Areas of Agreement / Disagreement

Participants express differing views on the sufficiency of example calculations to establish that y = x + 2 is one-to-one. The discussion remains unresolved regarding the broader implications of graphical analysis in confirming one-to-one functions.

Contextual Notes

Participants highlight the importance of understanding function graphs and their tests (horizontal and vertical line tests) but do not reach a consensus on the application of these concepts to the function in question.

mathdad
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Why is y = x + 2 one-to-one?
 
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No matter what x is the value of y will be a different answer.

y = x + 2

Let x = 0

y = 0 + 2

y = 2

(0, 2)

Let x = 3

y = 3 + 2

y = 5

(3, 5)

Yes, for every x value, y has a different, unique answer.

So, it is one-to-one. It is also linear because the biggest power is 1.

Correct?
 
fyi, using a few example function calculations does not confirm that a function is 1-1.

e.g. if you had "tested" using the same x-values with the function $y=\sqrt{9-x^2}$, you would have drawn an incorrect conclusion.

Having an idea of what the function graph looks like is important in determining things like domain, range, and whether or not a function is 1-1.

the function $y=\sqrt{9-x^2}$ is a semicircle of radius 3 in quadrants I and II ... it does not pass the horizontal line test.
 
It is important to have a picture in mind of the basic functions to help determine if it is one-to-one or not.

When is an expression not a function?
 
RTCNTC said:
It is important to have a picture in mind of the basic functions to help determine if it is one-to-one or not.

When is an expression not a function?

come on, you know this ... when its graph doesn't pass the vertical line test
 
Good information.
 

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